Is there a short book on learning proofs?

[Saladsamurai]

Is there a "short" book on learning proofs?

I realize that is probably an oxymoron I know that proofs take getting used to and lots of practice. However, I am in a bind here. I am an engineering student, so as you might imagine, I have almost never been asked to prove something mathematically. However, I am taking a graduate mathematical methods course and my professor thinks he is really funny. We never do anything proof-like in class, but they were all over our exam. Naturally, not one person out of 80 answered any of them.

I am kind of up to the challenge though. The problem is, there are only 4 weeks left until the final. I know I cannot completely master these things in such a short time, but I would like to make an effort to learn enough that I can at least write something when see one. I was hoping there might be a short book, or web resource that could give like the "top ten" approaches or things to look for when starting a proof. Even a if there is a longer text, but someone knows of a few good chapters that could give me an edge. Maybe the introductory chapters of a book you have read were the most helpful, or helped you learn how to get into the mindset of doing these.

Any suggestions are appreciated. Thanks!

 

[Petek]

You might want to take a look at the Wikipedia article on Mathematical proof. Some of the external links at the end of the article might be what you're looking for.

 

[SoItGoes]

I have to recommend this one by Velleman. It's really well done and you don't really need to read the entire book. The reading goes by really quick.

https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

 

[mathwonk]

the basic rule for doing a proof is to know the definitions cold.

i.e. to prove every wozzle is a wizzle, you just start by writing down the precise definition of a wozzle, and also that of a wizzle, and then you try to see why one being true forces the other also to be true.

in a math class, to prove something is true, you often have a theorem that has that something as its consequence. to apply it in a specific case, you then check that the hypotheses of that theorem hold in that case.

 

[fourier jr]

proofs & refutations by lakatos. it's probably not quite the most "short" or elementary, but it's good

 

[mathwonk]

a basic proof technique is by contradiction. so for this you must practice negating statements. e.g. to disprove that every wozzle is a wizzle, you must show there is at least one wozzle which is not a wizzle. so you only have to find one counterexample.

e.g. to disprove the false version of the fundamental theorem of aLGEBRA THAT EVERY COMPLEX POLYNOMIAL HAS A ROOT, just EXHIBIT THE constant POLYNOMIAL f(z) = 1.

 

[hadsed]

You could try 'How To Prove It', but that may be too basic to help, I can't be sure since you're an engineering student yet you're taking a high level maths class. It's by David Vellemen.

EDIT: Oops! Someone above recommended it already. Still, it's pretty good. Builds from the basics, if that's what you're looking for.

 

[Saladsamurai]

Thanks for all of the replies folks! I found a copy of How to Prove It for really cheap.